Mean Service time E(X) = 2 min.
\[E(X) = 1/\lambda = 2\]
So, \[\lambda = 2\]
\[ P(X>22) = e^{(-22\lambda)} \]
\[ P(X>22) = e^{(-22/2)} \]
\[ P(X>22) = e^{(-11)} \]
X be the total service time for 10 customers
\[ P(X>22) = 1 - P(X < 22) \]
\[ = 1 - \int_{0}^{22} (1/2) e^{-x/2} dt\]
\[ = 1 - 1/2 \Bigg[ e^{-x/2} / (-1/2) \Bigg]_{0}^{22} \]
\[ = 1 + \Bigg[ e^{-x/2} \Bigg]_{0}^{22} \] \[ = 1 + e^{-11} - e^{0} \]
exp(-11)## [1] 1.67017e-05